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  "body": "\n## Summary\n\nOperational calculus is a method that turns problems of analysis, above all linear differential and integral equations, into algebraic problems.\nThe differentiation operator is treated as an algebraic quantity, so an equation for the unknown function becomes an equation in a ring or field.\nIt is solved there by algebra, and the solution is translated back into a function.\nThe classical forms are the [[Heaviside operational calculus|QQ98C2AXZP]], its justification by the [[Laplace transform|0V49JEZW06]], and the [[Mikusiński operational calculus|TD5XK5AHNV]], which avoids integral transforms.\n\n## Explanations\n\n### L1 human\n\nThe idea is to treat \"take the derivative\" like multiplication by a number $s$.\nThen a differential equation such as $y' - 2y = 0$ with $y(0) = 1$ becomes the algebra problem $sY - 1 - 2Y = 0$, so $Y = 1/(s - 2)$.\nA table of translations says that $1/(s - 2)$ stands for the function $e^{2t}$, which is indeed the solution.\nEngineers used this kind of symbolic shortcut long before mathematicians made it rigorous.\n",
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